Correction of Arbitrary Field Errors in Population Inversion of Quantum Systems by Universal Composite Pulses

We introduce universal broadband composite pulse sequences for robust high-fidelity population inversion in two-state quantum systems, which compensate deviations in any parameter of the driving field (e.g., pulse amplitude, pulse duration, detuning from resonance, Stark shifts, unwanted frequency chirp, etc.) and are applicable with any pulse shape. We demonstrate the efficiency and universality of these composite pulses by experimental data on rephasing of atomic coherences in a ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal.

Figure 1

Numerically simulated infidelity $|U_{11}^{(n)}{|}^2$ vs static detuning and duration $T$ of each constituent pulse (referred to as “single pulse duration”) for a single pulse and several universal CPs (with rectangular shapes) from Table 1. The labels $m=1,2,4$ indicate the error level $10^{-m}$.

Figure 2

Numerically simulated (a),(b) and experimentally measured rephasing efficiency of stored light (c),(d) vs static detuning and single pulse duration $T$ for a single rectangular pulse (a),(c) and rectangular CP $U3$ (b),(d) with phases (0, $\pi /2$, 0) from Table 1. The Rabi frequency is kept fixed at ${\mathrm{\Omega }}_{\mathrm{rf}}\approx 2\pi \times 155\mathrm{kHz}$; i.e., a single $\pi$ pulse has a duration of $\tau =3.2\mu \mathrm{s}$.

Figure 3

Experimentally measured rephasing efficiency of stored light vs static detuning and single pulse duration for different universal CP sequences from Table 1 (labeled in each frame). The left column is for sequences of rectangular pulses and the right column is for sequences of Gaussian pulses. In either case the peak Rabi frequency is ${\mathrm{\Omega }}_{\mathrm{rf}}\approx 2\pi \times 155\mathrm{kHz}$. Hence, for rectangular pulses, the pulse duration of a perfect $\pi$ pulse is $\tau =3.2\mu \mathrm{s}$ and for Gaussian pulses, it is $2.8\mu \mathrm{s}$ (FWHM).

Figure 4

Numerically simulated (a),(b) and experimentally measured rephasing efficiency of stored light (c),(d) vs static detuning and chirp range, symmetric around resonance, of each constituent pulse for a single rectangular pulse (a),(c) and universal CP $U9b$ with phases from Table 1 (b),(d). The Rabi frequency is kept fixed at ${\mathrm{\Omega }}_{\mathrm{rf}}\approx 2\pi \times 155\mathrm{kHz}$ and the duration of each (constituent) pulse is $T=3.2\mu \mathrm{s}$.